. On a trip to Paris, Franco visits the Eiffel tower at 2:46 P.M. The Eiffel tower is 986 feet tall and Franco is 6 feet tall. Franco casts a shadow is 8 feet long. How long is the Eiffel tower's shadow(to the nearest foot)?
. On a trip to Paris, Franco visits the Eiffel tower at 2:46 P.M. The Eiffel tower is 986 feet tall and Franco is 6 feet tall. Franco casts a shadow is 8 feet long. How long is the Eiffel tower's shadow(to the nearest foot)?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**Problem 31:**
On a trip to Paris, Franco visits the Eiffel Tower at 2:46 P.M. The Eiffel Tower is 986 feet tall and Franco is 6 feet tall. Franco casts a shadow that is 8 feet long. How long is the Eiffel Tower’s shadow (to the nearest foot)?
**Explanation/Steps:**
- The problem involves finding the length of the Eiffel Tower's shadow using the principle of similar triangles.
- Since Franco and the Eiffel Tower are casting shadows at the same time, the triangles formed by them and their respective shadows are similar.
- We can use the proportion:
\[\frac{\text{Height of Franco}}{\text{Length of Franco's Shadow}} = \frac{\text{Height of Eiffel Tower}}{\text{Length of Eiffel Tower's Shadow}}\]
Substituting the known values:
\[\frac{6 \text{ ft}}{8 \text{ ft}} = \frac{986 \text{ ft}}{\text{Length of Eiffel Tower's Shadow}}\]
- Solving for the length of the Eiffel Tower's shadow:
\[\frac{6}{8} = \frac{986}{\text{Shadow Length}}\]
\[Shadow Length = \frac{986 \times 8}{6}\]
\[Shadow Length = \frac{7888}{6}\]
\[Shadow Length ≈ 1315\]
- Therefore, the Eiffel Tower's shadow is approximately 1,315 feet long.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf01151a-a752-463d-a4d4-89673a1f897f%2F4ece1a62-9695-40e3-8c89-4580a5f51fe4%2F9tspijb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 31:**
On a trip to Paris, Franco visits the Eiffel Tower at 2:46 P.M. The Eiffel Tower is 986 feet tall and Franco is 6 feet tall. Franco casts a shadow that is 8 feet long. How long is the Eiffel Tower’s shadow (to the nearest foot)?
**Explanation/Steps:**
- The problem involves finding the length of the Eiffel Tower's shadow using the principle of similar triangles.
- Since Franco and the Eiffel Tower are casting shadows at the same time, the triangles formed by them and their respective shadows are similar.
- We can use the proportion:
\[\frac{\text{Height of Franco}}{\text{Length of Franco's Shadow}} = \frac{\text{Height of Eiffel Tower}}{\text{Length of Eiffel Tower's Shadow}}\]
Substituting the known values:
\[\frac{6 \text{ ft}}{8 \text{ ft}} = \frac{986 \text{ ft}}{\text{Length of Eiffel Tower's Shadow}}\]
- Solving for the length of the Eiffel Tower's shadow:
\[\frac{6}{8} = \frac{986}{\text{Shadow Length}}\]
\[Shadow Length = \frac{986 \times 8}{6}\]
\[Shadow Length = \frac{7888}{6}\]
\[Shadow Length ≈ 1315\]
- Therefore, the Eiffel Tower's shadow is approximately 1,315 feet long.
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